Question

Solve, using formula:

x² + x – (a + 2)(a + 1) = 0

Answer 1

Given quadratic equation is x² + x – (a + 2)(a + 1) = 0

Using quadratic formula,

`=> x = (-1 ± sqrt(1^2 - 4(a + 2)(a + 1)))/2`

`=> x = (-1 ± sqrt(1 - 4 - (a^2 + 3a + 2)))/2`

`=> x = (-1 ± sqrt( 1 + 4a^2 + 12a + 8))/2`

`=> x = (-1 ± sqrt(4a^2 + 12a + 9))/2`

`=> x = (-1 ± sqrt((2a + 3)^2))/2`

`=> x = (-1 ± (2a + 3))/2`

`=> x = (-1 ± (2a + 3))/2` or `x = (-1 ± (2a + 3))/2`

`=> x = (2a + 2)/2` or `x = (-2a - 4)/2`

`=> x = (2( a + 1))/2` or `x = (2(-a -2))/2`

⇒ x = a + 1 or x = – a – 2 = – (a + 2)